List questions from local-field

Published on 29 May 2021 - 12:08

129

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In which field, minimal Weierstrass equation of elliptic curve can be defined?

Published on 26 Jun 2021 - 13:06

260

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What is the meaning of a finite $\pi$-adic expansion in a local number field?

Published on 06 Jul 2021 - 22:42

74

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p-th powers in $\mathbb{Q}_p(\zeta)$

Published on 07 Jul 2021 - 14:00

368

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Two versions of Hensel's lemma

Published on 25 Mar 2026 - 12:53

75

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Reduction types of $y^{2} = x^{3}+a_{6}$ over wildly ramified field extensions

Published on 27 Jul 2021 - 8:56

36

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Blow-up of origin of $K^2$ with $K$ a non-archimedian local field

Published on 26 Mar 2026 - 14:22

173

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Reference for Galois theory of local fields

Published on 01 Aug 2021 - 13:44

116

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Reduction of an elliptic curve $E/\mathbb{Q}_3$

Published on 14 Aug 2021 - 16:34

75

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The dense subgroup of ${\mathrm{Gal}}(\overline{{\Bbb Q}_p}/{\Bbb Q}_p)$.

Published on 15 Aug 2021 - 14:40

278

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Integer ring of local field is DVR?

Published on 25 Mar 2026 - 13:53

77

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$K_v(a^{1/m}) /K_v$ is unramified if only if $v(a)\equiv0 \pmod m$

Published on 25 Mar 2026 - 9:50

22

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Index $n$ subgroup of local field exists?

Published on 14 Sep 2021 - 17:38

314

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Completions of Global Field are Local Fields

Published on 14 Sep 2021 - 20:22

44

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Sufficient condition of $K'/K$ is ramified extension

Published on 27 Mar 2026 - 0:04

List Question

How to prove $v(x+y)\geq $inf$(v(x),v(y))$ in Serre's Local fields?

In which field, minimal Weierstrass equation of elliptic curve can be defined?

What is the meaning of a finite $\pi$-adic expansion in a local number field?

p-th powers in $\mathbb{Q}_p(\zeta)$

Two versions of Hensel's lemma

Reduction types of $y^{2} = x^{3}+a_{6}$ over wildly ramified field extensions

Blow-up of origin of $K^2$ with $K$ a non-archimedian local field

Reference for Galois theory of local fields

Reduction of an elliptic curve $E/\mathbb{Q}_3$

The dense subgroup of ${\mathrm{Gal}}(\overline{{\Bbb Q}_p}/{\Bbb Q}_p)$.

Integer ring of local field is DVR?

$K_v(a^{1/m}) /K_v$ is unramified if only if $v(a)\equiv0 \pmod m$

Index $n$ subgroup of local field exists?

Completions of Global Field are Local Fields

Sufficient condition of $K'/K$ is ramified extension

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